User:Binary198/Comparison between ordinal notations

An ordinal notation is a partial function from a finite alphabet to a countable set of ordinals. A Gödel numbering is a function from the set of well-formed formulae to the natural numbers. There are many such schemes of ordinal notations, including schemes by Wilhelm Ackermann, Heinz Bachmann, Wilfried Buchholz, Georg Cantor, Solomon Feferman, Gerhard Jäger and Wolfram Pohlers. This article is a comparison between various schemes of ordinal notation.

On the other hand, an ordinal collapsing function is a technique for defining certain large countable ordinals. Ordinal collapsing functions are typically denoted using some variation of either the Greek letter psi or theta. They are inextricably intertwined with the theory of ordinal analysis, as they are used to describe the strength of certain formal systems. Ordinal notations and ordinal collapsing functions are often confused: they are not the same, so in this article their strength will be compared.

Anyone who views this article, feel free to add your own notation/function.